第76章 对火星轨道变化问题的最后解释(10/14)

tsaremuchsmallerthanthoseofallnineplanets:theamplitudesoftheouterfiveplanetsaremuchlargerthanthoseoftheinnerplanets.thisdoesnotmeanthattheinnerterrestrialplanetarysubsystemismorestablethantheouterone:thisissimplyaresultoftherelativesmallnessofthemassesofthefourterrestrialplanetscomparedwiththoseoftheouterjovianplanets.anotherthingwenoticeisthattheinnerplanetarysubsystemmaybecomeunstablemorerapidlythantheouteronebecauseofitsshorterorbitaltime-scales.thiscanbeseeninthepanelsdenotedasinner4infig.7wherethelonger-periodicandirregularoscillationsaremoreapparentthaninthepanelsdenotedastotal9.actually，thefluctuationsintheinner4panelsaretoalargeextentasaresultoftheorbitalvariationofthemercury.however，wecannotneglectthecontributionfromotherterrestrialplanets，aswewillseeinsubsequentsections.
    4.4long-termcouplingofseveralneighbouringplanetpairs
    letusseesomeindividualvariationsofplanetaryorbitalenergyandangularmomentumexpressedbythelow-passfiltereddelaunayelements.figs10and11showlong-termevolutionoftheorbitalenergyofeachplanetandtheangularmomentuminn+1andn?2integrations.wenoticethatsomeplanetsformapparentpairsintermsoforbitalenergyandangularmomentumexchange.inparticular，venusandearthmakeatypicalpair.inthefigures，theyshownegativecorrelationsinexchangeofenergyandpositivecorrelationsinexchangeofangularmomentum.thenegativecorrelationinexchangeoforbitalenergymeansthatthetwoplanetsformacloseddynamicalsystemintermsoftheorbitalenergy.thepositivecorrelationinexchangeofangularmomentummeansthatthetwoplanetsaresimultaneouslyundercertainlong-termperturbations.candidatesforperturbersarejupiterandsaturn.alsoinfig.11，wecanseethatmarsshows'itivecorrelationintheangularmomentumvariationtothevenus–earthsystem.mercuryexhibitscertainnegativecorrelationsintheangularmomentumversusthevenus–earthsystem，whichseemstobeareactioncausedbytheconservationofangularmomentumintheterrestrialplanetarysubsystem.
    itisnotclearatthemomentwhythevenus–earthpairexhibitsanegativecorrelationinenergyexchan

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